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This is a bit like denying the English King Arthur because the bulk of them are descended from the Saxons that King Arthur was supposed to have been fightingNo, it's more like denying WASP Americans the native american heritage. Even ignoring the clouded history between the two groups, the former simply came later and have nothing to do with it.
>I don't see any compelling reason to say that the modern Greeks are more entitled to Alexander's legacy than the modern Macedonians, given that neither ethnic group is actually descended from Alexander (his family was all murdered).
The claims of legacy is not about having Alexander's family DNA - it's about historical tracing and culture and so on. In any case, even DNA wise, ancient to modern Greeks are quite close according to related studies (and unlike some western racist prejudices in the past centuries, dismissing modern Greeks right to their ancestry).
>and neither culture bears any resemblance to the culture of Alexander
Says who? Greeks have been speaking and developing the Greek culture and language since before the times of Alexander. And Greek vocabulary as developed at the time of Alexander's expansion, is still easily understood by modern Greeks.
Things did change, as they do everywhere - a culture changed after 2.3 millenia of development, is not the same as it being something alien that came from nowhere.
Does 16th or even 19th century US culture look like the modern one, if seen superficially? Not. However if traced back, and seen as a series of historical developments, it's a specific stream, discreet than say Mexican or Canadian culture or whatever. And that's just a few centuries. And of course, there being a big difference to 2024 US culture to 1780 US culture doesn't mean current Americans don't have a claim to the Founding Fathers, or Poe, or Mark Twain or whatever - or that suddenly Canadians can lay claim to those things.